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If (t- 8) is a factor of t^2 - kt - 48, then k=

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If (t- 8) is a factor of t^2 - kt - 48, then k= [#permalink] New post 24 Jan 2014, 02:53
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

If (t- 8) is a factor of t^2 - kt - 48, then k=

(A) - 6
(B) - 2
(C) 2
(D) 6
(E) 14

Problem Solving
Question: 57
Category: Algebra Second-degree equations
Page: 69
Difficulty: 600


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Re: If (t- 8) is a factor of t^2 - kt - 48, then k= [#permalink] New post 24 Jan 2014, 02:53
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SOLUTION

If (t- 8) is a factor of t^2 - kt - 48, then k=

(A) - 6
(B) - 2
(C) 2
(D) 6
(E) 14

\((t - 8)\) is a factor of \(t^2 - kt - 48\) means that \(t = 8\) is a solution of the equation \(t^2 - kt - 48 = 0\).

Substitute\(t = 8\) to get the value of k: \(8^2 - 8k - 48 = 0\) --> \(k = 2\).

Answer: C.
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Re: If (t- 8) is a factor of t^2 - kt - 48, then k= [#permalink] New post 24 Jan 2014, 04:55
Factoring the expression:
(t - 8) (t - ?), since (t - 8) is a factor, the other bracket has to be (t + 6).
The net result is -2. So (B)? Not sure of the answer because I got lost with the signs a bit.
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Re: If (t- 8) is a factor of t^2 - kt - 48, then k= [#permalink] New post 24 Jan 2014, 22:27
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Put the value of t-8=0, or t=8 in equation t^2+kt+48=0: Solving we get k=2.
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If (t- 8) is a factor of t^2 - kt - 48, then k= [#permalink] New post 24 Jan 2014, 23:46
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If (t- 8) is a factor of \(t^2 - kt - 48\), then k=

(A) - 6
(8) - 2
(C) 2
(0) 6
(E) 14


It is given that \((t - 8)\) is a factor of the quadratic expression \(t^2 - kt - 48\)
Hence, we need to find the other factor of \(-48\) such that the sum of factors is\(-(\frac{-k}{1})=k\).

Thus, \((8) * x = -48\)

Or, \(x = -6\)

So, \(k = 8 + (- 6) = 2\)

Answer: (C)

Last edited by arunspanda on 01 Nov 2014, 02:02, edited 1 time in total.
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Re: If (t- 8) is a factor of t^2 - kt - 48, then k= [#permalink] New post 25 Jan 2014, 11:39
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SOLUTION

If (t- 8) is a factor of t^2 - kt - 48, then k=

(A) - 6
(B) - 2
(C) 2
(D) 6
(E) 14

\((t - 8)\) is a factor of \(t^2 - kt - 48\) means that \(t = 8\) is a solution of the equation \(t^2 - kt - 48 = 0\).

Substitute\(t = 8\) to get the value of k: \(8^2 - 8k - 48 = 0\) --> \(k = 2\).

Answer: C.
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: If (t- 8) is a factor of t^2 - kt - 48, then k= [#permalink] New post 25 Feb 2014, 18:44
-8 x ?? = -48
?? = 6, so the other factor is 6
(t-8)(t+6) would be the two factors
-k = -8+6
-k = -2
k=2 Answer = C
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Re: If (t- 8) is a factor of t^2 - kt - 48, then k= [#permalink] New post 22 May 2014, 23:38
Vieta's formulas applied to quadratic: x1+x2= -b/a & x1*x2=c/a
From what is given in the question: 8+x2=k and 8*x2=-48
so, x2=-6 and thus 8-6=k i.e. k=2
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Re: If (t- 8) is a factor of t^2 - kt - 48, then k= [#permalink] New post 30 Jun 2015, 15:40
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Re: If (t- 8) is a factor of t^2 - kt - 48, then k= [#permalink] New post 30 Jun 2015, 21:27
since (t-8) is a factor, then: (8)^2 - 8k - 48 = 0,
-8k = -16
k = 2.
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Re: If (t- 8) is a factor of t^2 - kt - 48, then k=   [#permalink] 30 Jun 2015, 21:27
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